Reading assignment: 39.6

Look at the velocity transformation equation, Eqn 39.18 (8th edition). In the context of me throwing a ball forward while riding on a fast train (and being observed by the class on the ground), u_{x}' = the speed at which I throw the ball, v = the speed of the train, and u_{x} = the speed of the ball as measured by the class. Suppose I throw the ball at 0.5 c. What speed does the class observe the ball to travel at when the train is moving at 0.01 c? 0.50 c? 0.99 c? (Give 4 sig figs.) What do you learn from those answers? 0.01c --> 0.5075c (compare to 0.51c) 0.50c --> 0.8000c (compare to 1.00c) 0.99c --> 0.9967c (compare to 1.49c) For situations with small velocities, the answers are close to what Newton would predict. For situations with large velocities, the answer is always limited by the speed of light.